Key points are not available for this paper at this time.
A violation of the reciprocity relation, which induces a violation of the distance-duality relation, reflects itself in a change in the normalization of the cosmic microwave spectrum in such a way that its spectrum is grey. We show that existing observational constraints imply that the reciprocity relation cannot be violated by more than 0.01% between decoupling and today. We compare this effect to other sources of violation of the distance-duality relations which induce spectral distortion of the cosmic microwave background spectrum.
Ellis et al. (Fri,) studied this question.